On \(n\)-normed spaces
Summary: Given an \(n\)-normed space with \(n\geq 2\), we offer a simple way to derive an \((n-1)\)-norm from the \(n\)-norm and realize that any \(n\)-normed space is an \((n-1)\)-normed space. We also show that, in certain cases, the \((n-1)\)-norm can be derived from the \(n\)-norm in such a way that the convergence and completeness in the \(n\)-norm is equivalent to those in the derived \((n-1)\)-norm. Using this fact, we prove a fixed point theorem for some \(n\)-Banach spaces.
scientific article; zbMATH DE number 1740550